Answer:
Which is in form of
y=mx+c
[tex]y=\dfrac{x}{2}+5[/tex]
Step-by-step explanation:
Given:
Let,
point A( x₁ , y₁) ≡ ( 4 , 7)
point B( x₂ , y₂ )≡ (10 , 10)
To Find:
Equation of Line AB =?
Solution:
Equation of a line passing through a points A( x₁ , y₁) and point B( x₂ , y₂ ) is given by the formula Two -Point Form,
[tex](y-y_{1})=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }\times (x-x_{1})[/tex]
Now on substituting the slope and point A( x₁ , y₁) ≡ ( 4 ,7) and B( x₂ , y₂ )≡ (10 , 10) we get
[tex](y-10)=\dfrac{10-7}{10-4}\times (x-10)\\ \\y-10=\dfrac{3}{6}(x-10)\\\\2(y-10)=(x-10)\\2y-20=x-10\\\\y=\dfrac{x}{2}+5....Which\ is\ required[/tex]
Which is in form of
y=mx+c
[tex]y=\dfrac{x}{2}+5[/tex]
The equation of the line, in slope-intercept form, is: y = 1/2x + 5.
Given:
(4, 7) and (10, 10)
Slope (m) = change in y / change in x = (10 - 7) / (10 - 4)
Slope (m) = 3/6 = 1/2
Find "b" by substituting (x, y) = (4, 7) and m = 1/2 into y = mx + b:
7 = 1/2(4) + b
7 = 2 + b
7 - 2 = b
b = 5
Substitute m = 1/2, and b = 5 into y = mx + b.
y = 1/2x + 5
Therefore, the equation of the line, in slope-intercept form, is: y = 1/2x + 5.
Learn more about slope-intercept form on:
https://brainly.com/question/25826868
